{"id":1357,"date":"2019-01-14T03:03:22","date_gmt":"2019-01-14T03:03:22","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ivytech-sci111\/chapter\/specific-heat\/"},"modified":"2019-01-28T16:26:11","modified_gmt":"2019-01-28T16:26:11","slug":"specific-heat","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-sci111\/chapter\/specific-heat\/","title":{"raw":"Module 3 Specific Heat","rendered":"Module 3 Specific Heat"},"content":{"raw":"<div class=\"boundless-concept\">\r\n<h2>Heat Capacity<\/h2>\r\nThe heat capacity measures the amount of heat necessary to raise the temperature of an object or system by one degree Celsius.\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\nExplain the enthalpy in a system with constant volume and pressure\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Key Takeaways<\/h3>\r\n<h4>Key Points<\/h4>\r\n<ul>\r\n \t<li>Heat capacity is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount. It is measured in joules per Kelvin and given by.<\/li>\r\n \t<li>The heat capacity is an extensive property, scaling with the size of the system.<\/li>\r\n \t<li>The heat capacity of most systems is not constant (though it can often be treated as such). It depends on the temperature, pressure, and volume of the system under consideration.<\/li>\r\n<\/ul>\r\n<h4>Key Terms<\/h4>\r\n<ul>\r\n \t<li><strong>heat capacity<\/strong>: The amount of heat energy needed to raise the temperature of an object or unit of matter by one degree Celsius; in units of joules per kelvin (J\/K).<\/li>\r\n \t<li><strong>enthalpy<\/strong>: the total amount of energy in a system, including both the internal energy and the energy needed to displace its environment<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h3>Heat Capacity<\/h3>\r\nHeat capacity (usually denoted by a capital C, often with subscripts), or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount. In SI units, heat capacity is expressed in units of joules per kelvin (J\/K).\r\n\r\nAn object's heat capacity (symbol <em>C<\/em>) is defined as the ratio of the amount of heat energy transferred to an object to the resulting increase in temperature of the object.\r\n\r\n[latex]\\displaystyle{\\text{C}=\\frac{\\text{Q}}{ \\Delta \\text{T}}.} [\/latex]\r\n\r\nHeat capacity is an extensive property, so it scales with the size of the system. A sample containing twice the amount of substance as another sample requires the transfer of twice as much heat (Q) to achieve the same change in temperature (\u0394T). For example, if it takes 1,000 J to heat a block of iron, it would take 2,000 J to heat a second block of iron with twice the mass as the first.\r\n<h3>The Measurement of Heat Capacity<\/h3>\r\nThe heat capacity of most systems is not a constant. Rather, it depends on the state variables of the thermodynamic system under study. In particular, it is dependent on temperature itself, as well as on the pressure and the volume of the system, and the ways in which pressures and volumes have been allowed to change while the system has passed from one temperature to another. The reason for this is that pressure-volume work done to the system raises its temperature by a mechanism other than heating, while pressure-volume work done by the system absorbs heat without raising the system's temperature. (The temperature dependence is why the definition a calorie is formally the energy needed to heat 1 g of water from 14.5 to 15.5 \u00b0C instead of generally by 1 \u00b0C. )\r\n\r\nDifferent measurements of heat capacity can therefore be performed, most commonly at constant pressure and constant volume. The values thus measured are usually subscripted (by p and V, respectively) to indicate the definition. Gases and liquids are typically also measured at constant volume. Measurements under constant pressure produce larger values than those at constant volume because the constant pressure values also include heat energy that is used to do work to expand the substance against the constant pressure as its temperature increases. This difference is particularly notable in gases where values under constant pressure are typically 30% to 66.7% greater than those at constant volume.\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"boundless-concept\">\r\n<h2>Specific Heat<\/h2>\r\nThe specific heat is an intensive property that describes how much heat must be added to a particular substance to raise its temperature.\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\nSummarize the quantitative relationship between heat transfer and temperature change\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Key Takeaways<\/h3>\r\n<h4>Key Points<\/h4>\r\n<ul>\r\n \t<li>Unlike the total heat capacity, the specific heat capacity is independent of mass or volume. It describes how much heat must be added to a unit of mass of a given substance to raise its temperature by one degree Celsius. The units of specific heat capacity are J\/(kg \u00b0C) or equivalently J\/(kg K).<\/li>\r\n \t<li>The heat capacity and the specific heat are related by C=cm or c=C\/m.<\/li>\r\n \t<li>The mass m, specific heat c, change in temperature \u0394T, and heat added (or subtracted) Q are related by the equation: Q=mc\u0394T.<\/li>\r\n \t<li>Values of specific heat are dependent on the properties and phase of a given substance. Since they cannot be calculated easily, they are empirically measured and available for reference in tables.<\/li>\r\n<\/ul>\r\n<h4>Key Terms<\/h4>\r\n<ul>\r\n \t<li><strong>specific heat capacity<\/strong>: The amount of heat that must be added (or removed) from a unit mass of a substance to change its temperature by one degree Celsius. It is an intensive property.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h3>Specific Heat<\/h3>\r\nThe heat capacity is an extensive property that describes how much heat energy it takes to raise the temperature of a given system. However, it would be pretty inconvenient to measure the heat capacity of every unit of matter. What we want is an intensive property that depends only on the type and phase of a substance and can be applied to systems of arbitrary size. This quantity is known as the specific heat capacity (or simply, the specific heat), which is the heat capacity per unit mass of a material. Experiments show that the transferred heat depends on three factors: (1) The change in temperature, (2) the mass of the system, and (3) the substance and phase of the substance. The last two factors are encapsulated in the value of the specific heat.\r\n<div class=\"wp-caption aligncenter\" style=\"width: 520px\">\r\n<div class=\"figure-cont\">\r\n\r\n<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2548\/2019\/01\/14030305\/figure-15-02-01.jpeg\" alt=\"image\" width=\"510\" height=\"618\" \/>\r\n<p class=\"wp-caption-text\"><strong>Heat Transfer and Specific Heat Capacity<\/strong>: The heat Q transferred to cause a temperature change depends on the magnitude of the temperature change, the mass of the system, and the substance and phase involved. (a) The amount of heat transferred is directly proportional to the temperature change. To double the temperature change of a mass m, you need to add twice the heat. (b) The amount of heat transferred is also directly proportional to the mass. To cause an equivalent temperature change in a doubled mass, you need to add twice the heat. (c) The amount of heat transferred depends on the substance and its phase. If it takes an amount Q of heat to cause a temperature change \u0394T in a given mass of copper, it will take 10.8 times that amount of heat to cause the equivalent temperature change in the same mass of water assuming no phase change in either substance.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"embed-wrap\">\r\n<div class=\"figure-cont\">\r\n<div>http:\/\/www.youtube.com\/watch?v=Kbn_WHEJsyc<\/div>\r\n<strong>Specific Heat Capacity<\/strong>: This lesson relates heat to a change in temperature. We discuss how the amount of heat needed for a temperature change is dependent on mass and the substance involved, and that relationship is represented by the specific heat capactiy of the substance, C.\r\n\r\n<\/div>\r\n<\/div>\r\nThe dependence on temperature change and mass are easily understood. Because the (average) kinetic energy of an atom or molecule is proportional to the absolute temperature, the internal energy of a system is proportional to the absolute temperature and the number of atoms or molecules. Since the transferred heat is equal to the change in the internal energy, the heat is proportional to the mass of the substance and the temperature change. The transferred heat also depends on the substance so that, for example, the heat necessary to raise the temperature is less for alcohol than for water. For the same substance, the transferred heat also depends on the phase (gas, liquid, or solid).\r\n\r\nThe quantitative relationship between heat transfer and temperature change contains all three factors:\r\n\r\n[latex]\\text{Q}=\\text{mc}\\Delta \\text{T}[\/latex],\r\n\r\nwhere Q is the symbol for heat transfer, m is the mass of the substance, and \u0394T is the change in temperature. The symbol c stands for specific heat and depends on the material and phase.\r\n\r\nThe specific heat is the amount of heat necessary to change the temperature of 1.00 kg of mass by 1.00\u00baC. The specific heat c is a property of the substance; its SI unit is J\/(kg\u22c5K) or J\/(kg\u22c5C). Recall that the temperature change (\u0394T) is the same in units of kelvin and degrees Celsius. Note that the total heat capacity C is simply the product of the specific heat capacity c and the mass of the substance m, i.e.,\r\n\r\n[latex]\\text{C}=\\text{mc}[\/latex] or [latex]\\text{c}=\\frac{\\text{C}}{\\text{m}}=\\frac{\\text{C}}{\\rho \\text{V}}[\/latex],\r\n\r\nwhere \u03f1 is the density of the substance and V is its volume.\r\n\r\nValues of specific heat must generally be looked up in tables, because there is no simple way to calculate them. Instead, they are measured empirically. In general, the specific heat also depends on the temperature. The table below lists representative values of specific heat for various substances. Except for gases, the temperature and volume dependence of the specific heat of most substances is weak. The specific heat of water is five times that of glass and ten times that of iron, which means that it takes five times as much heat to raise the temperature of water the same amount as for glass and ten times as much heat to raise the temperature of water as for iron. In fact, water has one of the largest specific heats of any material, which is important for sustaining life on Earth.\r\n<div class=\"wp-caption aligncenter\" style=\"width: 364px\">\r\n<div class=\"figure-cont\">\r\n\r\n<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2548\/2019\/01\/14030308\/specificheats.png\" alt=\"image\" width=\"354\" height=\"804\" \/>\r\n<p class=\"wp-caption-text\"><strong>Specific Heats<\/strong>: Listed are the specific heats of various substances. These values are identical in units of cal\/(g\u22c5C).3. cv at constant volume and at 20.0\u00baC, except as noted, and at 1.00 atm average pressure. Values in parentheses are cp at a constant pressure of 1.00 atm.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"boundless-concept\">\r\n<h2>Calorimetry<\/h2>\r\nCalorimetry is the measurement of the heat of chemical reactions or physical changes.\r\n<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\nAnalyze the relationship between the gas constant for an ideal gas yield and volume\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Key Takeaways<\/h3>\r\n<h4>Key Points<\/h4>\r\n<ul>\r\n \t<li>A calorimeter is used to measure the heat generated (or absorbed) by a physical change or chemical reaction. The science of measuring these changes is known as calorimetry.<\/li>\r\n \t<li>In order to do calorimetry, it is crucial to know the specific heats of the substances being measured.<\/li>\r\n \t<li>Calorimetry can be performed under constant volume or constant pressure. The type of calculation done depends on the conditions of the experiment.<\/li>\r\n<\/ul>\r\n<h4>Key Terms<\/h4>\r\n<ul>\r\n \t<li><strong>constant-pressure calorimeter<\/strong>: An instrument used to measure the heat generated during changes that do not involve changes in pressure.<\/li>\r\n \t<li><strong>calorimeter<\/strong>: An apparatus for measuring the heat generated or absorbed by either a chemical reaction, change of phase or some other physical change.<\/li>\r\n \t<li><strong>constant-volume calorimeter<\/strong>: An instrument used to measure the heat generated during changes that do not involve changes in volume.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h3>Calorimetry<\/h3>\r\n<h3>Overview<\/h3>\r\nCalorimetry is the science of measuring the heat of chemical reactions or physical changes. Calorimetry is performed with a calorimeter. A simple calorimeter just consists of a thermometer attached to a metal container full of water suspended above a combustion chamber. The word calorimetry is derived from the Latin word <em>calor<\/em>, meaning heat. Scottish physician and scientist Joseph Black, who was the first to recognize the distinction between heat and temperature, is said to be the founder of calorimetry.\r\n\r\nCalorimetry requires that the material being heated have known thermal properties, i.e. specific heat capacities. The classical rule, recognized by Clausius and by Kelvin, is that the pressure exerted by the calorimetric material is fully and rapidly determined solely by its temperature and volume; this rule is for changes that do not involve phase change, such as melting of ice. There are many materials that do not comply with this rule, and for them, more complex equations are required than those below.\r\n<div class=\"wp-caption alignleft\" style=\"width: 303px\">\r\n<div class=\"figure-cont\">\r\n\r\n<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2548\/2019\/01\/14030311\/ice-calorimeter.jpeg\" alt=\"image\" width=\"293\" height=\"491\" \/>\r\n<p class=\"wp-caption-text\"><strong>Ice Calorimeter<\/strong>: The world's first ice-calorimeter, used in the winter of 1782-83, by Antoine Lavoisier and Pierre-Simon Laplace, to determine the heat evolved in variouschemical changes; calculations which were based on Joseph Black's prior discovery of latent heat. These experiments mark the foundation of thermochemistry.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<h3>Basic Calorimetry at Constant Value<\/h3>\r\nConstant-volume calorimetry is calorimetry performed at a constant volume. This involves the use of a constant-volume calorimeter (one type is called a Bomb calorimeter). For constant-volume calorimetry:\r\n\r\n[latex]\\delta \\text{Q}=\\text{C}_{\\text{V}}\\Delta \\text{T}=\\text{mc}_{\\text{V}}\\Delta \\text{T}[\/latex]\r\n\r\nwhere \u03b4Q is the increment of heat gained by the sample, C<sub>V<\/sub> is the heat capacity at constant volume, c<sub>v<\/sub> is the specific heat at constant volume, and \u0394T is the change in temperature.\r\n<h3>Measuring Enthalpy Change<\/h3>\r\nTo find the enthalpy change per mass (or per mole) of a substance A in a reaction between two substances A and B, the substances are added to a calorimeter and the initial and final temperatures (before the reaction started and after it has finished) are noted. Multiplying the temperature change by the mass and specific heat capacities of the substances gives a value for the energy given off or absorbed during the reaction:\r\n\r\n[latex]\\delta \\text{Q}=\\Delta \\text{T}(\\text{m}_{\\text{A}}\\text{c}_{\\text{A}}+\\text{m}_{\\text{B}}\\text{c}_{\\text{B}})[\/latex]\r\n\r\nDividing the energy change by how many grams (or moles) of A were present gives its enthalpy change of reaction. This method is used primarily in academic teaching as it describes the theory of calorimetry. It does not account for the heat loss through the container or the heat capacity of the thermometer and container itself. In addition, the object placed inside the calorimeter shows that the objects transferred their heat to the calorimeter and into the liquid, and the heat absorbed by the calorimeter and the liquid is equal to the heat given off by the metals.\r\n<h3>Constant-Pressure Calorimetry<\/h3>\r\nA constant-pressure calorimeter measures the change in enthalpy of a reaction occurring in solution during which the atmospheric pressure remains constant. An example is a coffee-cup calorimeter, which is constructed from two nested Styrofoam cups and a lid with two holes, allowing insertion of a thermometer and a stirring rod. The inner cup holds a known amount of a solute, usually water, that absorbs the heat from the reaction. When the reaction occurs, the outer cup provides insulation. Then\r\n\r\n[latex]\\text{C}_{\\text{P}}=\\frac{\\text{W}\\Delta \\text{H}}{\\text{M}\\Delta \\text{T}}[\/latex]\r\n\r\nwhere C<sub>p<\/sub> is the specific heat at constant pressure, \u0394H is the enthalpy of the solution, \u0394T is the change in temperature, W is the mass of the solute, and M is the molecular mass of the solute. The measurement of heat using a simple calorimeter, like the coffee cup calorimeter, is an example of constant-pressure calorimetry, since the pressure (atmospheric pressure) remains constant during the process. Constant-pressure calorimetry is used in determining the changes in enthalpy occurring in solution. Under these conditions the change in enthalpy equals the heat (Q=\u0394H).\r\n\r\n<\/div>\r\n<div class=\"boundless-concept\"><\/div>\r\n<div class=\"boundless-concept\">\r\n\r\n&nbsp;\r\n\r\n<\/div>","rendered":"<div class=\"boundless-concept\">\n<h2>Heat Capacity<\/h2>\n<p>The heat capacity measures the amount of heat necessary to raise the temperature of an object or system by one degree Celsius.<\/p>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>Explain the enthalpy in a system with constant volume and pressure<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Key Takeaways<\/h3>\n<h4>Key Points<\/h4>\n<ul>\n<li>Heat capacity is the measurable physical quantity that characterizes the amount of heat required to change a substance&#8217;s temperature by a given amount. It is measured in joules per Kelvin and given by.<\/li>\n<li>The heat capacity is an extensive property, scaling with the size of the system.<\/li>\n<li>The heat capacity of most systems is not constant (though it can often be treated as such). It depends on the temperature, pressure, and volume of the system under consideration.<\/li>\n<\/ul>\n<h4>Key Terms<\/h4>\n<ul>\n<li><strong>heat capacity<\/strong>: The amount of heat energy needed to raise the temperature of an object or unit of matter by one degree Celsius; in units of joules per kelvin (J\/K).<\/li>\n<li><strong>enthalpy<\/strong>: the total amount of energy in a system, including both the internal energy and the energy needed to displace its environment<\/li>\n<\/ul>\n<\/div>\n<h3>Heat Capacity<\/h3>\n<p>Heat capacity (usually denoted by a capital C, often with subscripts), or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance&#8217;s temperature by a given amount. In SI units, heat capacity is expressed in units of joules per kelvin (J\/K).<\/p>\n<p>An object&#8217;s heat capacity (symbol <em>C<\/em>) is defined as the ratio of the amount of heat energy transferred to an object to the resulting increase in temperature of the object.<\/p>\n<p>[latex]\\displaystyle{\\text{C}=\\frac{\\text{Q}}{ \\Delta \\text{T}}.}[\/latex]<\/p>\n<p>Heat capacity is an extensive property, so it scales with the size of the system. A sample containing twice the amount of substance as another sample requires the transfer of twice as much heat (Q) to achieve the same change in temperature (\u0394T). For example, if it takes 1,000 J to heat a block of iron, it would take 2,000 J to heat a second block of iron with twice the mass as the first.<\/p>\n<h3>The Measurement of Heat Capacity<\/h3>\n<p>The heat capacity of most systems is not a constant. Rather, it depends on the state variables of the thermodynamic system under study. In particular, it is dependent on temperature itself, as well as on the pressure and the volume of the system, and the ways in which pressures and volumes have been allowed to change while the system has passed from one temperature to another. The reason for this is that pressure-volume work done to the system raises its temperature by a mechanism other than heating, while pressure-volume work done by the system absorbs heat without raising the system&#8217;s temperature. (The temperature dependence is why the definition a calorie is formally the energy needed to heat 1 g of water from 14.5 to 15.5 \u00b0C instead of generally by 1 \u00b0C. )<\/p>\n<p>Different measurements of heat capacity can therefore be performed, most commonly at constant pressure and constant volume. The values thus measured are usually subscripted (by p and V, respectively) to indicate the definition. Gases and liquids are typically also measured at constant volume. Measurements under constant pressure produce larger values than those at constant volume because the constant pressure values also include heat energy that is used to do work to expand the substance against the constant pressure as its temperature increases. This difference is particularly notable in gases where values under constant pressure are typically 30% to 66.7% greater than those at constant volume.<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"boundless-concept\">\n<h2>Specific Heat<\/h2>\n<p>The specific heat is an intensive property that describes how much heat must be added to a particular substance to raise its temperature.<\/p>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>Summarize the quantitative relationship between heat transfer and temperature change<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Key Takeaways<\/h3>\n<h4>Key Points<\/h4>\n<ul>\n<li>Unlike the total heat capacity, the specific heat capacity is independent of mass or volume. It describes how much heat must be added to a unit of mass of a given substance to raise its temperature by one degree Celsius. The units of specific heat capacity are J\/(kg \u00b0C) or equivalently J\/(kg K).<\/li>\n<li>The heat capacity and the specific heat are related by C=cm or c=C\/m.<\/li>\n<li>The mass m, specific heat c, change in temperature \u0394T, and heat added (or subtracted) Q are related by the equation: Q=mc\u0394T.<\/li>\n<li>Values of specific heat are dependent on the properties and phase of a given substance. Since they cannot be calculated easily, they are empirically measured and available for reference in tables.<\/li>\n<\/ul>\n<h4>Key Terms<\/h4>\n<ul>\n<li><strong>specific heat capacity<\/strong>: The amount of heat that must be added (or removed) from a unit mass of a substance to change its temperature by one degree Celsius. It is an intensive property.<\/li>\n<\/ul>\n<\/div>\n<h3>Specific Heat<\/h3>\n<p>The heat capacity is an extensive property that describes how much heat energy it takes to raise the temperature of a given system. However, it would be pretty inconvenient to measure the heat capacity of every unit of matter. What we want is an intensive property that depends only on the type and phase of a substance and can be applied to systems of arbitrary size. This quantity is known as the specific heat capacity (or simply, the specific heat), which is the heat capacity per unit mass of a material. Experiments show that the transferred heat depends on three factors: (1) The change in temperature, (2) the mass of the system, and (3) the substance and phase of the substance. The last two factors are encapsulated in the value of the specific heat.<\/p>\n<div class=\"wp-caption aligncenter\" style=\"width: 520px\">\n<div class=\"figure-cont\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2548\/2019\/01\/14030305\/figure-15-02-01.jpeg\" alt=\"image\" width=\"510\" height=\"618\" \/><\/p>\n<p class=\"wp-caption-text\"><strong>Heat Transfer and Specific Heat Capacity<\/strong>: The heat Q transferred to cause a temperature change depends on the magnitude of the temperature change, the mass of the system, and the substance and phase involved. (a) The amount of heat transferred is directly proportional to the temperature change. To double the temperature change of a mass m, you need to add twice the heat. (b) The amount of heat transferred is also directly proportional to the mass. To cause an equivalent temperature change in a doubled mass, you need to add twice the heat. (c) The amount of heat transferred depends on the substance and its phase. If it takes an amount Q of heat to cause a temperature change \u0394T in a given mass of copper, it will take 10.8 times that amount of heat to cause the equivalent temperature change in the same mass of water assuming no phase change in either substance.<\/p>\n<\/div>\n<\/div>\n<div class=\"embed-wrap\">\n<div class=\"figure-cont\">\n<div>http:\/\/www.youtube.com\/watch?v=Kbn_WHEJsyc<\/div>\n<p><strong>Specific Heat Capacity<\/strong>: This lesson relates heat to a change in temperature. We discuss how the amount of heat needed for a temperature change is dependent on mass and the substance involved, and that relationship is represented by the specific heat capactiy of the substance, C.<\/p>\n<\/div>\n<\/div>\n<p>The dependence on temperature change and mass are easily understood. Because the (average) kinetic energy of an atom or molecule is proportional to the absolute temperature, the internal energy of a system is proportional to the absolute temperature and the number of atoms or molecules. Since the transferred heat is equal to the change in the internal energy, the heat is proportional to the mass of the substance and the temperature change. The transferred heat also depends on the substance so that, for example, the heat necessary to raise the temperature is less for alcohol than for water. For the same substance, the transferred heat also depends on the phase (gas, liquid, or solid).<\/p>\n<p>The quantitative relationship between heat transfer and temperature change contains all three factors:<\/p>\n<p>[latex]\\text{Q}=\\text{mc}\\Delta \\text{T}[\/latex],<\/p>\n<p>where Q is the symbol for heat transfer, m is the mass of the substance, and \u0394T is the change in temperature. The symbol c stands for specific heat and depends on the material and phase.<\/p>\n<p>The specific heat is the amount of heat necessary to change the temperature of 1.00 kg of mass by 1.00\u00baC. The specific heat c is a property of the substance; its SI unit is J\/(kg\u22c5K) or J\/(kg\u22c5C). Recall that the temperature change (\u0394T) is the same in units of kelvin and degrees Celsius. Note that the total heat capacity C is simply the product of the specific heat capacity c and the mass of the substance m, i.e.,<\/p>\n<p>[latex]\\text{C}=\\text{mc}[\/latex] or [latex]\\text{c}=\\frac{\\text{C}}{\\text{m}}=\\frac{\\text{C}}{\\rho \\text{V}}[\/latex],<\/p>\n<p>where \u03f1 is the density of the substance and V is its volume.<\/p>\n<p>Values of specific heat must generally be looked up in tables, because there is no simple way to calculate them. Instead, they are measured empirically. In general, the specific heat also depends on the temperature. The table below lists representative values of specific heat for various substances. Except for gases, the temperature and volume dependence of the specific heat of most substances is weak. The specific heat of water is five times that of glass and ten times that of iron, which means that it takes five times as much heat to raise the temperature of water the same amount as for glass and ten times as much heat to raise the temperature of water as for iron. In fact, water has one of the largest specific heats of any material, which is important for sustaining life on Earth.<\/p>\n<div class=\"wp-caption aligncenter\" style=\"width: 364px\">\n<div class=\"figure-cont\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2548\/2019\/01\/14030308\/specificheats.png\" alt=\"image\" width=\"354\" height=\"804\" \/><\/p>\n<p class=\"wp-caption-text\"><strong>Specific Heats<\/strong>: Listed are the specific heats of various substances. These values are identical in units of cal\/(g\u22c5C).3. cv at constant volume and at 20.0\u00baC, except as noted, and at 1.00 atm average pressure. Values in parentheses are cp at a constant pressure of 1.00 atm.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"boundless-concept\">\n<h2>Calorimetry<\/h2>\n<p>Calorimetry is the measurement of the heat of chemical reactions or physical changes.<\/p>\n<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>Analyze the relationship between the gas constant for an ideal gas yield and volume<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Key Takeaways<\/h3>\n<h4>Key Points<\/h4>\n<ul>\n<li>A calorimeter is used to measure the heat generated (or absorbed) by a physical change or chemical reaction. The science of measuring these changes is known as calorimetry.<\/li>\n<li>In order to do calorimetry, it is crucial to know the specific heats of the substances being measured.<\/li>\n<li>Calorimetry can be performed under constant volume or constant pressure. The type of calculation done depends on the conditions of the experiment.<\/li>\n<\/ul>\n<h4>Key Terms<\/h4>\n<ul>\n<li><strong>constant-pressure calorimeter<\/strong>: An instrument used to measure the heat generated during changes that do not involve changes in pressure.<\/li>\n<li><strong>calorimeter<\/strong>: An apparatus for measuring the heat generated or absorbed by either a chemical reaction, change of phase or some other physical change.<\/li>\n<li><strong>constant-volume calorimeter<\/strong>: An instrument used to measure the heat generated during changes that do not involve changes in volume.<\/li>\n<\/ul>\n<\/div>\n<h3>Calorimetry<\/h3>\n<h3>Overview<\/h3>\n<p>Calorimetry is the science of measuring the heat of chemical reactions or physical changes. Calorimetry is performed with a calorimeter. A simple calorimeter just consists of a thermometer attached to a metal container full of water suspended above a combustion chamber. The word calorimetry is derived from the Latin word <em>calor<\/em>, meaning heat. Scottish physician and scientist Joseph Black, who was the first to recognize the distinction between heat and temperature, is said to be the founder of calorimetry.<\/p>\n<p>Calorimetry requires that the material being heated have known thermal properties, i.e. specific heat capacities. The classical rule, recognized by Clausius and by Kelvin, is that the pressure exerted by the calorimetric material is fully and rapidly determined solely by its temperature and volume; this rule is for changes that do not involve phase change, such as melting of ice. There are many materials that do not comply with this rule, and for them, more complex equations are required than those below.<\/p>\n<div class=\"wp-caption alignleft\" style=\"width: 303px\">\n<div class=\"figure-cont\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2548\/2019\/01\/14030311\/ice-calorimeter.jpeg\" alt=\"image\" width=\"293\" height=\"491\" \/><\/p>\n<p class=\"wp-caption-text\"><strong>Ice Calorimeter<\/strong>: The world&#8217;s first ice-calorimeter, used in the winter of 1782-83, by Antoine Lavoisier and Pierre-Simon Laplace, to determine the heat evolved in variouschemical changes; calculations which were based on Joseph Black&#8217;s prior discovery of latent heat. These experiments mark the foundation of thermochemistry.<\/p>\n<\/div>\n<\/div>\n<h3>Basic Calorimetry at Constant Value<\/h3>\n<p>Constant-volume calorimetry is calorimetry performed at a constant volume. This involves the use of a constant-volume calorimeter (one type is called a Bomb calorimeter). For constant-volume calorimetry:<\/p>\n<p>[latex]\\delta \\text{Q}=\\text{C}_{\\text{V}}\\Delta \\text{T}=\\text{mc}_{\\text{V}}\\Delta \\text{T}[\/latex]<\/p>\n<p>where \u03b4Q is the increment of heat gained by the sample, C<sub>V<\/sub> is the heat capacity at constant volume, c<sub>v<\/sub> is the specific heat at constant volume, and \u0394T is the change in temperature.<\/p>\n<h3>Measuring Enthalpy Change<\/h3>\n<p>To find the enthalpy change per mass (or per mole) of a substance A in a reaction between two substances A and B, the substances are added to a calorimeter and the initial and final temperatures (before the reaction started and after it has finished) are noted. Multiplying the temperature change by the mass and specific heat capacities of the substances gives a value for the energy given off or absorbed during the reaction:<\/p>\n<p>[latex]\\delta \\text{Q}=\\Delta \\text{T}(\\text{m}_{\\text{A}}\\text{c}_{\\text{A}}+\\text{m}_{\\text{B}}\\text{c}_{\\text{B}})[\/latex]<\/p>\n<p>Dividing the energy change by how many grams (or moles) of A were present gives its enthalpy change of reaction. This method is used primarily in academic teaching as it describes the theory of calorimetry. It does not account for the heat loss through the container or the heat capacity of the thermometer and container itself. In addition, the object placed inside the calorimeter shows that the objects transferred their heat to the calorimeter and into the liquid, and the heat absorbed by the calorimeter and the liquid is equal to the heat given off by the metals.<\/p>\n<h3>Constant-Pressure Calorimetry<\/h3>\n<p>A constant-pressure calorimeter measures the change in enthalpy of a reaction occurring in solution during which the atmospheric pressure remains constant. An example is a coffee-cup calorimeter, which is constructed from two nested Styrofoam cups and a lid with two holes, allowing insertion of a thermometer and a stirring rod. The inner cup holds a known amount of a solute, usually water, that absorbs the heat from the reaction. When the reaction occurs, the outer cup provides insulation. Then<\/p>\n<p>[latex]\\text{C}_{\\text{P}}=\\frac{\\text{W}\\Delta \\text{H}}{\\text{M}\\Delta \\text{T}}[\/latex]<\/p>\n<p>where C<sub>p<\/sub> is the specific heat at constant pressure, \u0394H is the enthalpy of the solution, \u0394T is the change in temperature, W is the mass of the solute, and M is the molecular mass of the solute. The measurement of heat using a simple calorimeter, like the coffee cup calorimeter, is an example of constant-pressure calorimetry, since the pressure (atmospheric pressure) remains constant during the process. Constant-pressure calorimetry is used in determining the changes in enthalpy occurring in solution. Under these conditions the change in enthalpy equals the heat (Q=\u0394H).<\/p>\n<\/div>\n<div class=\"boundless-concept\"><\/div>\n<div class=\"boundless-concept\">\n<p>&nbsp;<\/p>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1357\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Curation and Revision. <strong>Provided by<\/strong>: Boundless.com. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Heat capacity. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Heat_capacity\">http:\/\/en.wikipedia.org\/wiki\/Heat_capacity<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>enthalpy. <strong>Provided by<\/strong>: Wiktionary. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wiktionary.org\/wiki\/enthalpy\">http:\/\/en.wiktionary.org\/wiki\/enthalpy<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>heat capacity. <strong>Provided by<\/strong>: Wiktionary. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wiktionary.org\/wiki\/heat_capacity\">http:\/\/en.wiktionary.org\/wiki\/heat_capacity<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>OpenStax College, College Physics. September 18, 2013. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m42224\/latest\/?collection=col11406\/1.7\">http:\/\/cnx.org\/content\/m42224\/latest\/?collection=col11406\/1.7<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Heat capacity. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Heat_capacity\">http:\/\/en.wikipedia.org\/wiki\/Heat_capacity<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>specific heat capacity. <strong>Provided by<\/strong>: Wiktionary. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wiktionary.org\/wiki\/specific_heat_capacity\">http:\/\/en.wiktionary.org\/wiki\/specific_heat_capacity<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Specific Heat Capacity. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.youtube.com\/watch?v=Kbn_WHEJsyc\">http:\/\/www.youtube.com\/watch?v=Kbn_WHEJsyc<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em>. <strong>License Terms<\/strong>: Standard YouTube license<\/li><li>OpenStax College, College Physics. October 14, 2012. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m42224\/latest\/?collection=col11406\/1.7\">http:\/\/cnx.org\/content\/m42224\/latest\/?collection=col11406\/1.7<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>OpenStax College, College Physics. October 14, 2012. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m42224\/latest\/?collection=col11406\/1.7\">http:\/\/cnx.org\/content\/m42224\/latest\/?collection=col11406\/1.7<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Calorimetry. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Calorimetry\">http:\/\/en.wikipedia.org\/wiki\/Calorimetry<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Calorimeter. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Calorimeter\">http:\/\/en.wikipedia.org\/wiki\/Calorimeter<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>calorimeter. <strong>Provided by<\/strong>: Wiktionary. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wiktionary.org\/wiki\/calorimeter\">http:\/\/en.wiktionary.org\/wiki\/calorimeter<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Boundless. <strong>Provided by<\/strong>: Boundless Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.boundless.com\/\/physics\/definition\/constant-volume-calorimeter\">http:\/\/www.boundless.com\/\/physics\/definition\/constant-volume-calorimeter<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>constant-pressure calorimeter. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/constant-pressure%20calorimeter\">http:\/\/en.wikipedia.org\/wiki\/constant-pressure%20calorimeter<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Specific Heat Capacity. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.youtube.com\/watch?v=Kbn_WHEJsyc\">http:\/\/www.youtube.com\/watch?v=Kbn_WHEJsyc<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em>. <strong>License Terms<\/strong>: Standard YouTube license<\/li><li>OpenStax College, College Physics. October 14, 2012. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m42224\/latest\/?collection=col11406\/1.7\">http:\/\/cnx.org\/content\/m42224\/latest\/?collection=col11406\/1.7<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>OpenStax College, College Physics. October 14, 2012. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m42224\/latest\/?collection=col11406\/1.7\">http:\/\/cnx.org\/content\/m42224\/latest\/?collection=col11406\/1.7<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Calorimetry. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Calorimetry\">http:\/\/en.wikipedia.org\/wiki\/Calorimetry<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em><\/li><li>specific heat. <strong>Provided by<\/strong>: Wiktionary. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wiktionary.org\/wiki\/specific_heat\">http:\/\/en.wiktionary.org\/wiki\/specific_heat<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Specific heat. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Specific_heat\">http:\/\/en.wikipedia.org\/wiki\/Specific_heat<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Ideal gas. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Ideal_gas\">http:\/\/en.wikipedia.org\/wiki\/Ideal_gas<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Relations between heat capacities. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Relations_between_heat_capacities\">http:\/\/en.wikipedia.org\/wiki\/Relations_between_heat_capacities<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Julius Robert von Mayer. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Julius_Robert_von_Mayer\">http:\/\/en.wikipedia.org\/wiki\/Julius_Robert_von_Mayer<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>adiabatic index. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/adiabatic%20index\">http:\/\/en.wikipedia.org\/wiki\/adiabatic%20index<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Fundamental Thermodynamic Relation. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Fundamental%20Thermodynamic%20Relation\">http:\/\/en.wikipedia.org\/wiki\/Fundamental%20Thermodynamic%20Relation<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Specific Heat Capacity. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.youtube.com\/watch?v=Kbn_WHEJsyc\">http:\/\/www.youtube.com\/watch?v=Kbn_WHEJsyc<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em>. <strong>License Terms<\/strong>: Standard YouTube license<\/li><li>OpenStax College, College Physics. October 14, 2012. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m42224\/latest\/?collection=col11406\/1.7\">http:\/\/cnx.org\/content\/m42224\/latest\/?collection=col11406\/1.7<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>OpenStax College, College Physics. 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October 13, 2015. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/85abf193-2bd2-4908-8563-90b8a7ac8df6@9.110\">http:\/\/cnx.org\/contents\/85abf193-2bd2-4908-8563-90b8a7ac8df6@9.110<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>combustion. <strong>Provided by<\/strong>: Wiktionary. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wiktionary.org\/wiki\/combustion\">http:\/\/en.wiktionary.org\/wiki\/combustion<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Specific Heat Capacity. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.youtube.com\/watch?v=Kbn_WHEJsyc\">http:\/\/www.youtube.com\/watch?v=Kbn_WHEJsyc<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em>. <strong>License Terms<\/strong>: Standard YouTube license<\/li><li>OpenStax College, College Physics. October 14, 2012. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m42224\/latest\/?collection=col11406\/1.7\">http:\/\/cnx.org\/content\/m42224\/latest\/?collection=col11406\/1.7<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>OpenStax College, College Physics. October 14, 2012. <strong>Provided by<\/strong>: OpenStax CNX. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/content\/m42224\/latest\/?collection=col11406\/1.7\">http:\/\/cnx.org\/content\/m42224\/latest\/?collection=col11406\/1.7<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Calorimetry. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Calorimetry\">http:\/\/en.wikipedia.org\/wiki\/Calorimetry<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em><\/li><li>Julius Robert von Mayer. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/Julius_Robert_von_Mayer\">http:\/\/en.wikipedia.org\/wiki\/Julius_Robert_von_Mayer<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em><\/li><li>Thermally Agitated Molecule. <strong>Provided by<\/strong>: Wikipedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/en.wikipedia.org\/wiki\/File:Thermally_Agitated_Molecule.gif\">http:\/\/en.wikipedia.org\/wiki\/File:Thermally_Agitated_Molecule.gif<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Bomb Calorimeter. <strong>Provided by<\/strong>: Wikimedia. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/commons.wikimedia.org\/wiki\/File:Bomb_Calorimeter.png\">http:\/\/commons.wikimedia.org\/wiki\/File:Bomb_Calorimeter.png<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":18,"menu_order":5,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Heat capacity\",\"author\":\"\",\"organization\":\"Wikipedia\",\"url\":\"http:\/\/en.wikipedia.org\/wiki\/Heat_capacity\",\"project\":\"\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"enthalpy\",\"author\":\"\",\"organization\":\"Wiktionary\",\"url\":\"http:\/\/en.wiktionary.org\/wiki\/enthalpy\",\"project\":\"\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"heat capacity\",\"author\":\"\",\"organization\":\"Wiktionary\",\"url\":\"http:\/\/en.wiktionary.org\/wiki\/heat_capacity\",\"project\":\"\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"OpenStax College, College Physics. 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